Question

The volume as a function of time is given by v(t)=9/14t. Determine the inverse relationship so that the amount of time it will take to reach a given volume can be found.

Answer 1

To find the inverse relationship for the volume function v(t)=9/14t, multiply both sides by 14/9 to solve for t, resulting in the inverse function t(V) = (14/9)V. This equation allows us to calculate the elapsed time for a given volume.

Step-by-step explanation:

To find the inverse relationship of the volume as a function of time, given by v(t)=9/14t, we need to express the time t as a function of the volume V. This allows us to determine the amount of time it will take to reach a given volume.

Starting with the equation v(t) = 9/14t, we solve for t:

1. Multiply both sides by 14/9 to isolate t on one side of the equation. This gives us t = (14/9)v.
2. Therefore, the inverse function, which will give us time as a function of volume, is t(V) = (14/9)V.

This inverse function can now be used to find the elapsed time for any given volume V.